sbplib: +scheme/Elastic2dVariableAnisotropic.m annotate

annotate +scheme/Elastic2dVariableAnisotropic.m @ 1335:8d9fc7981796 feature/D2_boundary_opt

Calculate width for all orders

author	Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date	Sat, 07 May 2022 10:41:22 +0200
parents	a38e80fdbf60
children	da61892884a4

rev	line source
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	1 classdef Elastic2dVariableAnisotropic < scheme.Scheme
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	2
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	3 % Discretizes the elastic wave equation:
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	4 % rho u_{i,tt} = dj C_{ijkl} dk u_j
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	5 % opSet should be cell array of opSets, one per dimension. This
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	6 % is useful if we have periodic BC in one direction.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	7 % Assumes fully compatible operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	8
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	9 properties
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	10 m % Number of points in each direction, possibly a vector
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	11 h % Grid spacing
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	12
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	13 grid
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	14 dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	15
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	16 order % Order of accuracy for the approximation
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	17
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	18 % Diagonal matrices for variable coefficients
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	19 RHO, RHOi, RHOi_kron % Density
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	20 C % Elastic stiffness tensor
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	21
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	22 D % Total operator
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	23 D1 % First derivatives
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	24 % D2 % Second derivatives
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	25
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	26 % Boundary operators in cell format, used for BC
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	27 T_w, T_e, T_s, T_n
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	28
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	29 % Traction operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	30 tau_w, tau_e, tau_s, tau_n % Return vector field
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	31 tau1_w, tau1_e, tau1_s, tau1_n % Return scalar field
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	32 tau2_w, tau2_e, tau2_s, tau2_n % Return scalar field
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	33
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	34 % Inner products
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	35 H, Hi, Hi_kron, H_1D
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	36
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	37 % Boundary inner products (for scalar field)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	38 H_w, H_e, H_s, H_n
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	39
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	40 % Boundary restriction operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	41 e_w, e_e, e_s, e_n % Act on vector field, return vector field at boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	42 e1_w, e1_e, e1_s, e1_n % Act on vector field, return scalar field at boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	43 e2_w, e2_e, e2_s, e2_n % Act on vector field, return scalar field at boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	44 e_scalar_w, e_scalar_e, e_scalar_s, e_scalar_n; % Act on scalar field, return scalar field
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	45
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	46 % E{i}^T picks out component i
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	47 E
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	48
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	49 % Borrowing constants of the form gamma*h, where gamma is a dimensionless constant.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	50 h11 % First entry in norm matrix
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	51
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	52 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	53
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	54 methods
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	55
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	56 % The coefficients can either be function handles or grid functions
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	57 % optFlag -- if true, extra computations are performed, which may be helpful for optimization.
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	58 function obj = Elastic2dVariableAnisotropic(g, order, rho, C, opSet, optFlag, hollow)
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	59 default_arg('hollow', false);
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	60 default_arg('rho', @(x,y) 0*x+1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	61 default_arg('opSet',{@sbp.D2VariableCompatible, @sbp.D2VariableCompatible});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	62 default_arg('optFlag', false);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	63 dim = 2;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	64
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	65 C_default = cell(dim,dim,dim,dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	66 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	67 for j = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	68 for k = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	69 for l = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	70 C_default{i,j,k,l} = @(x,y) 0*x + 1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	71 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	72 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	73 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	74 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	75 default_arg('C', C_default);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	76 assert(isa(g, 'grid.Cartesian'))
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	77
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	78 if isa(rho, 'function_handle')
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	79 rho = grid.evalOn(g, rho);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	80 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	81
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	82 C_mat = cell(dim,dim,dim,dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	83 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	84 for j = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	85 for k = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	86 for l = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	87 if isa(C{i,j,k,l}, 'function_handle')
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	88 C{i,j,k,l} = grid.evalOn(g, C{i,j,k,l});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	89 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	90 C_mat{i,j,k,l} = spdiag(C{i,j,k,l});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	91 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	92 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	93 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	94 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	95 obj.C = C_mat;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	96
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	97 m = g.size();
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	98 m_tot = g.N();
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	99 lim = g.lim;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	100 if isempty(lim)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	101 x = g.x;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	102 lim = cell(length(x),1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	103 for i = 1:length(x)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	104 lim{i} = {min(x{i}), max(x{i})};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	105 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	106 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	107
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	108 % 1D operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	109 ops = cell(dim,1);
1303 49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	110 opsHollow = cell(dim,1);
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	111 h = zeros(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	112 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	113 ops{i} = opSet{i}(m(i), lim{i}, order);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	114 h(i) = ops{i}.h;
1303 49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	115 if hollow
49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	116 opsHollow{i} = sbp.D2VariableCompatibleHollow(m(i), lim{i}, order);
49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	117 end
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	118 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	119
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	120 % Borrowing constants
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	121 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	122 obj.h11{i} = h(i)*ops{i}.borrowing.H11;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	123 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	124
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	125 I = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	126 D1 = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	127 D2 = cell(dim,1);
1303 49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	128 D2Hollow = cell(dim,1);
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	129 H = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	130 Hi = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	131 e_0 = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	132 e_m = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	133 d1_0 = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	134 d1_m = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	135
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	136 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	137 I{i} = speye(m(i));
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	138 D1{i} = ops{i}.D1;
1303 49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	139 if hollow
49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	140 D2Hollow{i} = opsHollow{i}.D2;
49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	141 end
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	142 D2{i} = ops{i}.D2;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	143 H{i} = ops{i}.H;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	144 Hi{i} = ops{i}.HI;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	145 e_0{i} = ops{i}.e_l;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	146 e_m{i} = ops{i}.e_r;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	147 d1_0{i} = ops{i}.d1_l;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	148 d1_m{i} = ops{i}.d1_r;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	149 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	150
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	151 %====== Assemble full operators ========
1206 6b203030fb37 Fix performance (full matrices) issues in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	152 I_dim = speye(dim, dim);
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	153 RHO = spdiag(rho);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	154 obj.RHO = RHO;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	155 obj.RHOi = inv(RHO);
1206 6b203030fb37 Fix performance (full matrices) issues in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	156 obj.RHOi_kron = kron(obj.RHOi, I_dim);
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	157
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	158 obj.D1 = cell(dim,1);
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	159 D2_temp = cell(dim,dim,dim);
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	160
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	161 % D1
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	162 obj.D1{1} = kron(D1{1},I{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	163 obj.D1{2} = kron(I{1},D1{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	164
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	165 % Boundary restriction operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	166 e_l = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	167 e_r = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	168 e_l{1} = kron(e_0{1}, I{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	169 e_l{2} = kron(I{1}, e_0{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	170 e_r{1} = kron(e_m{1}, I{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	171 e_r{2} = kron(I{1}, e_m{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	172
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	173 e_scalar_w = e_l{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	174 e_scalar_e = e_r{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	175 e_scalar_s = e_l{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	176 e_scalar_n = e_r{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	177
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	178 e_w = kron(e_scalar_w, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	179 e_e = kron(e_scalar_e, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	180 e_s = kron(e_scalar_s, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	181 e_n = kron(e_scalar_n, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	182
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	183 % E{i}^T picks out component i.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	184 E = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	185 I = speye(m_tot,m_tot);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	186 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	187 e = sparse(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	188 e(i) = 1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	189 E{i} = kron(I,e);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	190 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	191 obj.E = E;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	192
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	193 e1_w = (e_scalar_w'*E{1}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	194 e1_e = (e_scalar_e'*E{1}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	195 e1_s = (e_scalar_s'*E{1}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	196 e1_n = (e_scalar_n'*E{1}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	197
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	198 e2_w = (e_scalar_w'*E{2}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	199 e2_e = (e_scalar_e'*E{2}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	200 e2_s = (e_scalar_s'*E{2}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	201 e2_n = (e_scalar_n'*E{2}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	202
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	203
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	204 % D2
1335 8d9fc7981796 Calculate width for all orders Vidar Stiernström <vidar.stiernstrom@it.uu.se> parents: 1304 diff changeset	205 width = order+1;
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	206 switch order
89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	207 case 2
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	208 nBP = 2;
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	209 case 4
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	210 nBP = 6;
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	211 case 6
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	212 nBP = 9;
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	213 end
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	214 for j = 1:dim
1206 6b203030fb37 Fix performance (full matrices) issues in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	215 for k = 1:dim
6b203030fb37 Fix performance (full matrices) issues in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	216 for l = 1:dim
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	217 if hollow
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	218 D2_temp{j,k,l} = sparse(m_tot, m_tot);
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	219 else
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	220 D2_temp{j,k,l} = spalloc(m_tot, m_tot, width*m_tot);
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	221 end
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	222 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	223 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	224 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	225 ind = grid.funcToMatrix(g, 1:m_tot);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	226
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	227 k = 1;
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	228 if hollow
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	229 mask = sparse(m(1), m(1));
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	230 mask(1:nBP, 1:nBP) = speye(nBP, nBP);
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	231 mask(end-nBP+1:end, end-nBP+1:end) = speye(nBP, nBP);
1304 a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	232 maskXSmall = kron(mask, speye(m(2), m(2)));
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	233 maskX = E{1}maskXSmallE{1}' + E{2}maskXSmallE{2}';
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	234 end
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	235 for r = 1:m(2)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	236 p = ind(:,r);
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	237 for j = 1:dim
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	238 for l = 1:dim
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	239 coeff = C{k,j,k,l};
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	240 if hollow && r > nBP && r < m(2) - nBP + 1
1303 49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	241 D_kk = D2Hollow{1}(coeff(p));
49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	242 else
49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	243 D_kk = D2{1}(coeff(p));
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	244 end
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	245 D2_temp{j,k,l}(p,p) = D_kk;
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	246 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	247 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	248 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	249
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	250 k = 2;
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	251 if hollow
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	252 mask = sparse(m(2), m(2));
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	253 mask(1:nBP, 1:nBP) = speye(nBP, nBP);
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	254 mask(end-nBP+1:end, end-nBP+1:end) = speye(nBP, nBP);
1304 a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	255 maskYSmall = kron(speye(m(1), m(1)), mask);
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	256
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	257 maskY = E{1}maskYSmallE{1}' + E{2}maskYSmallE{2}';
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	258 mask = maskX + maskY;
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	259 mask = mask>0;
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	260
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	261 maskSmall = maskXSmall + maskYSmall;
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	262 maskSmall = maskSmall>0;
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	263 end
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	264 for r = 1:m(1)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	265 p = ind(r,:);
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	266 for j = 1:dim
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	267 for l = 1:dim
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	268 coeff = C{k,j,k,l};
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	269 if hollow && r > nBP && r < m(1) - nBP + 1
1303 49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	270 D_kk = D2Hollow{2}(coeff(p));
49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	271 else
49e3870335ef Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet Martin Almquist <malmquist@stanford.edu> parents: 1302 diff changeset	272 D_kk = D2{2}(coeff(p));
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	273 end
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	274 D2_temp{j,k,l}(p,p) = D_kk;
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	275 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	276 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	277 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	278
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	279 % Quadratures
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	280 obj.H = kron(H{1},H{2});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	281 obj.Hi = inv(obj.H);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	282 obj.H_w = H{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	283 obj.H_e = H{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	284 obj.H_s = H{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	285 obj.H_n = H{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	286 obj.H_1D = {H{1}, H{2}};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	287
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	288 % Differentiation matrix D (without SAT)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	289 D1 = obj.D1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	290 D = sparse(dimm_tot,dimm_tot);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	291 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	292 for j = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	293 for k = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	294 for l = 1:dim
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	295 if i == k
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	296 D = D + E{j}D2_temp{j,k,l}E{l}';
89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	297 D2_temp{j,k,l} = [];
1206 6b203030fb37 Fix performance (full matrices) issues in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	298 else
1304 a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	299 if hollow
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	300 D = D + E{j}(maskSmallD1{i})C_mat{i,j,k,l}D1{k}*E{l}';
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	301 else
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	302 D = D + E{j}(D1{i})C_mat{i,j,k,l}D1{k}E{l}';
a38e80fdbf60 Improve performance for the hollow case Martin Almquist <malmquist@stanford.edu> parents: 1303 diff changeset	303 end
1206 6b203030fb37 Fix performance (full matrices) issues in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	304 end
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	305 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	306 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	307 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	308 end
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	309 clear D2_temp;
1302 a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	310 if hollow
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	311 mask = maskX + maskY;
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	312 mask = mask>0;
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	313 D = mask*D;
a0d615bde7f8 Add the hollow option to the anisotropic diffops Martin Almquist <malmquist@stanford.edu> parents: 1260 diff changeset	314 end
1206 6b203030fb37 Fix performance (full matrices) issues in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	315 D = obj.RHOi_kron*D;
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	316 obj.D = D;
1253 89dad61cad22 Make Elastic2dVariable faster and more memory efficient Martin Almquist <malmquist@stanford.edu> parents: 1252 diff changeset	317 clear D;
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	318 %=========================================%'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	319
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	320 % Numerical traction operators for BC.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	321 %
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	322 % Formula at boundary j: % tau^{j}_i = sum_l T^{j}_{il} u_l
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	323 %
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	324 T_l = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	325 T_r = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	326 tau_l = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	327 tau_r = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	328
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	329 D1 = obj.D1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	330
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	331 % Boundary j
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	332 for j = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	333 T_l{j} = cell(dim,dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	334 T_r{j} = cell(dim,dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	335 tau_l{j} = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	336 tau_r{j} = cell(dim,1);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	337
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	338 [~, n_l] = size(e_l{j});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	339 [~, n_r] = size(e_r{j});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	340
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	341 % Traction component i
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	342 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	343 tau_l{j}{i} = sparse(dim*m_tot, n_l);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	344 tau_r{j}{i} = sparse(dim*m_tot, n_r);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	345
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	346 % Displacement component l
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	347 for l = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	348 T_l{j}{i,l} = sparse(m_tot, n_l);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	349 T_r{j}{i,l} = sparse(m_tot, n_r);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	350
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	351 % Derivative direction k
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	352 for k = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	353 T_l{j}{i,l} = T_l{j}{i,l} ...
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	354 - (e_l{j}'C_mat{j,i,k,l}D1{k})';
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	355 T_r{j}{i,l} = T_r{j}{i,l} ...
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	356 + (e_r{j}'C_mat{j,i,k,l}D1{k})';
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	357 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	358 tau_l{j}{i} = tau_l{j}{i} + (T_l{j}{i,l}'*E{l}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	359 tau_r{j}{i} = tau_r{j}{i} + (T_r{j}{i,l}'*E{l}')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	360 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	361 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	362 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	363
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	364 % Traction tensors, T_ij
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	365 obj.T_w = T_l{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	366 obj.T_e = T_r{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	367 obj.T_s = T_l{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	368 obj.T_n = T_r{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	369
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	370 % Restriction operators
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	371 obj.e_w = e_w;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	372 obj.e_e = e_e;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	373 obj.e_s = e_s;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	374 obj.e_n = e_n;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	375
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	376 obj.e1_w = e1_w;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	377 obj.e1_e = e1_e;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	378 obj.e1_s = e1_s;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	379 obj.e1_n = e1_n;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	380
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	381 obj.e2_w = e2_w;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	382 obj.e2_e = e2_e;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	383 obj.e2_s = e2_s;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	384 obj.e2_n = e2_n;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	385
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	386 obj.e_scalar_w = e_scalar_w;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	387 obj.e_scalar_e = e_scalar_e;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	388 obj.e_scalar_s = e_scalar_s;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	389 obj.e_scalar_n = e_scalar_n;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	390
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	391 % First component of traction
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	392 obj.tau1_w = tau_l{1}{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	393 obj.tau1_e = tau_r{1}{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	394 obj.tau1_s = tau_l{2}{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	395 obj.tau1_n = tau_r{2}{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	396
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	397 % Second component of traction
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	398 obj.tau2_w = tau_l{1}{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	399 obj.tau2_e = tau_r{1}{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	400 obj.tau2_s = tau_l{2}{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	401 obj.tau2_n = tau_r{2}{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	402
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	403 % Traction vectors
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	404 obj.tau_w = (e_w'e1_wobj.tau1_w')' + (e_w'e2_wobj.tau2_w')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	405 obj.tau_e = (e_e'e1_eobj.tau1_e')' + (e_e'e2_eobj.tau2_e')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	406 obj.tau_s = (e_s'e1_sobj.tau1_s')' + (e_s'e2_sobj.tau2_s')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	407 obj.tau_n = (e_n'e1_nobj.tau1_n')' + (e_n'e2_nobj.tau2_n')';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	408
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	409 % Kroneckered norms and coefficients
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	410 obj.Hi_kron = kron(obj.Hi, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	411
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	412 % Misc.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	413 obj.m = m;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	414 obj.h = h;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	415 obj.order = order;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	416 obj.grid = g;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	417 obj.dim = dim;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	418
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	419 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	420
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	421
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	422 % Closure functions return the operators applied to the own domain to close the boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	423 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	424 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	425 % bc is a cell array of component and bc type, e.g. {1, 'd'} for Dirichlet condition
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	426 % on the first component. Can also be e.g.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	427 % {'normal', 'd'} or {'tangential', 't'} for conditions on
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	428 % tangential/normal component.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	429 % data is a function returning the data that should be applied at the boundary.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	430 % neighbour_scheme is an instance of Scheme that should be interfaced to.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	431 % neighbour_boundary is a string specifying which boundary to interface to.
1203 25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	432
25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	433 % For displacement bc:
25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	434 % bc = {comp, 'd', dComps},
25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	435 % where
25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	436 % dComps = vector of components with displacement BC. Default: 1:dim.
25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	437 % In this way, we can specify one BC at a time even though the SATs depend on all BC.
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	438 function [closure, penalty] = boundary_condition(obj, boundary, bc, tuning)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	439 default_arg('tuning', 1.0);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	440
1202 31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	441 assert( iscell(bc), 'The BC type must be a 2x1 or 3x1 cell array' );
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	442 comp = bc{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	443 type = bc{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	444 if ischar(comp)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	445 comp = obj.getComponent(comp, boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	446 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	447
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	448 e = obj.getBoundaryOperatorForScalarField('e', boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	449 tau = obj.getBoundaryOperator(['tau' num2str(comp)], boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	450 T = obj.getBoundaryTractionOperator(boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	451 h11 = obj.getBorrowing(boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	452 H_gamma = obj.getBoundaryQuadratureForScalarField(boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	453 nu = obj.getNormal(boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	454
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	455 E = obj.E;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	456 Hi = obj.Hi;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	457 RHOi = obj.RHOi;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	458 C = obj.C;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	459
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	460 dim = obj.dim;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	461 m_tot = obj.grid.N();
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	462
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	463 % Preallocate
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	464 [~, col] = size(tau);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	465 closure = sparse(dimm_tot, dimm_tot);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	466 penalty = sparse(dim*m_tot, col);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	467
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	468 j = comp;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	469 switch type
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	470
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	471 % Dirichlet boundary condition
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	472 case {'D','d','dirichlet','Dirichlet','displacement','Displacement'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	473
1202 31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	474 if numel(bc) >= 3
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	475 dComps = bc{3};
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	476 else
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	477 dComps = 1:dim;
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	478 end
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	479
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	480 % Loops over components that Dirichlet penalties end up on
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	481 % Y: symmetrizing part of penalty
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	482 % Z: symmetric part of penalty
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	483 % X = Y + Z.
1202 31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	484
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	485 % Nonsymmetric part goes on all components to
1203 25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	486 % yield traction in discrete energy rate
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	487 for i = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	488 Y = T{j,i}';
1202 31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	489 X = e*Y;
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	490 closure = closure + E{i}RHOiHiX'eH_gamma(e'*E{j}' );
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	491 penalty = penalty - E{i}RHOiHiX'e*H_gamma;
31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	492 end
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	493
1203 25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	494 % Symmetric part only required on components with displacement BC.
25cadc69a589 Update comments in Anisotropic Martin Almquist <malmquist@stanford.edu> parents: 1202 diff changeset	495 % (Otherwise it's not symmetric.)
1202 31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	496 for i = dComps
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	497 Z = sparse(m_tot, m_tot);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	498 for l = 1:dim
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	499 for k = 1:dim
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	500 Z = Z + nu(l)C{l,i,k,j}nu(k);
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	501 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	502 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	503 Z = -tuningdim/h11Z;
1202 31d7288d0653 Make Anisotropic work for mixed displacement/traction BC at the same boundary. Martin Almquist <malmquist@stanford.edu> parents: 1201 diff changeset	504 X = Z;
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	505 closure = closure + E{i}RHOiHiX'eH_gamma(e'*E{j}' );
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	506 penalty = penalty - E{i}RHOiHiX'e*H_gamma;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	507 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	508
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	509 % Free boundary condition
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	510 case {'F','f','Free','free','traction','Traction','t','T'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	511 closure = closure - E{j}RHOiHieH_gamma*tau';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	512 penalty = penalty + E{j}RHOiHieH_gamma;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	513
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	514 % Unknown boundary condition
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	515 otherwise
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	516 error('No such boundary condition: type = %s',type);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	517 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	518 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	519
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	520 % type Struct that specifies the interface coupling.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	521 % Fields:
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	522 % -- tuning: penalty strength, defaults to 1.0
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	523 % -- interpolation: type of interpolation, default 'none'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	524 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	525
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	526 defaultType.tuning = 1.0;
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	527 defaultType.interpolation = 'none';
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	528 default_struct('type', defaultType);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	529
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	530 switch type.interpolation
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	531 case {'none', ''}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	532 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	533 case {'op','OP'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	534 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	535 otherwise
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	536 error('Unknown type of interpolation: %s ', type.interpolation);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	537 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	538 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	539
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	540 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	541 tuning = type.tuning;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	542
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	543 % u denotes the solution in the own domain
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	544 % v denotes the solution in the neighbour domain
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	545
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	546 u = obj;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	547 v = neighbour_scheme;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	548
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	549 % Operators, u side
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	550 e_u = u.getBoundaryOperatorForScalarField('e', boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	551 tau_u = u.getBoundaryOperator('tau', boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	552 h11_u = u.getBorrowing(boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	553 nu_u = u.getNormal(boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	554
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	555 E_u = u.E;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	556 C_u = u.C;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	557 m_tot_u = u.grid.N();
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	558
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	559 % Operators, v side
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	560 e_v = v.getBoundaryOperatorForScalarField('e', neighbour_boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	561 tau_v = v.getBoundaryOperator('tau', neighbour_boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	562 h11_v = v.getBorrowing(neighbour_boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	563 nu_v = v.getNormal(neighbour_boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	564
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	565 E_v = v.E;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	566 C_v = v.C;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	567 m_tot_v = v.grid.N();
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	568
1252 8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	569 % Fix {'e', 's'}, {'w', 'n'}, and {'x','x'} couplings
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	570 flipFlag = false;
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	571 e_v_flip = e_v;
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	572 if (strcmp(boundary,'s') && strcmp(neighbour_boundary,'e')) \|\| ...
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	573 (strcmp(boundary,'e') && strcmp(neighbour_boundary,'s')) \|\| ...
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	574 (strcmp(boundary,'w') && strcmp(neighbour_boundary,'n')) \|\| ...
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	575 (strcmp(boundary,'n') && strcmp(neighbour_boundary,'w')) \|\| ...
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	576 (strcmp(boundary,'s') && strcmp(neighbour_boundary,'s')) \|\| ...
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	577 (strcmp(boundary,'n') && strcmp(neighbour_boundary,'n')) \|\| ...
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	578 (strcmp(boundary,'w') && strcmp(neighbour_boundary,'w')) \|\| ...
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	579 (strcmp(boundary,'e') && strcmp(neighbour_boundary,'e'))
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	580
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	581 flipFlag = true;
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	582 e_v_flip = fliplr(e_v);
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	583
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	584 t1 = tau_v(:,1:2:end-1);
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	585 t2 = tau_v(:,2:2:end);
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	586
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	587 t1 = fliplr(t1);
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	588 t2 = fliplr(t2);
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	589
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	590 tau_v(:,1:2:end-1) = t1;
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	591 tau_v(:,2:2:end) = t2;
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	592 end
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	593
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	594 % Operators that are only required for own domain
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	595 Hi = u.Hi_kron;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	596 RHOi = u.RHOi_kron;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	597 e_kron = u.getBoundaryOperator('e', boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	598 T_u = u.getBoundaryTractionOperator(boundary);
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	599
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	600 % Shared operators
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	601 H_gamma = u.getBoundaryQuadratureForScalarField(boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	602 H_gamma_kron = u.getBoundaryQuadrature(boundary);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	603 dim = u.dim;
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	604
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	605 % Preallocate
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	606 [~, m_int] = size(H_gamma);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	607 closure = sparse(dimm_tot_u, dimm_tot_u);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	608 penalty = sparse(dimm_tot_u, dimm_tot_v);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	609
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	610 % ---- Continuity of displacement ------
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	611
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	612 % Y: symmetrizing part of penalty
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	613 % Z: symmetric part of penalty
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	614 % X = Y + Z.
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	615
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	616 % Loop over components to couple across interface
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	617 for j = 1:dim
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	618
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	619 % Loop over components that penalties end up on
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	620 for i = 1:dim
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	621 Y = 1/2*T_u{j,i}';
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	622 Z_u = sparse(m_int, m_int);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	623 Z_v = sparse(m_int, m_int);
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	624 for l = 1:dim
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	625 for k = 1:dim
1207 05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	626 Z_u = Z_u + e_u'nu_u(l)C_u{l,i,k,j}nu_u(k)e_u;
05a01f77d0e3 Swap indices and fix bug in ElasticVariableAnisotropic Martin Almquist <malmquist@stanford.edu> parents: 1204 diff changeset	627 Z_v = Z_v + e_v'nu_v(l)C_v{l,i,k,j}nu_v(k)e_v;
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	628 end
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	629 end
1252 8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	630
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	631 if flipFlag
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	632 Z_v = rot90(Z_v,2);
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	633 end
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	634
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	635 Z = -tuningdim( 1/(4h11_u)Z_u + 1/(4h11_v)Z_v );
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	636 X = Y + Z*e_u';
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	637 closure = closure + E_u{i}X'H_gammae_u'E_u{j}';
1252 8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	638 penalty = penalty - E_u{i}X'H_gammae_v_flip'E_v{j}';
8fc2f9a4c882 Add (temporary) fix for e-s , w-n, and x-x couplings Martin Almquist <malmquist@stanford.edu> parents: 1208 diff changeset	639
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	640 end
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	641 end
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	642
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	643 % ---- Continuity of traction ------
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	644 closure = closure - 1/2e_kronH_gamma_kron*tau_u';
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	645 penalty = penalty - 1/2e_kronH_gamma_kron*tau_v';
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	646
1204 687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	647 % ---- Multiply by inverse of density x quadraure ----
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	648 closure = RHOiHiclosure;
687515778437 Add anisotropic interface Martin Almquist <malmquist@stanford.edu> parents: 1203 diff changeset	649 penalty = RHOiHipenalty;
1201 8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	650
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	651 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	652
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	653 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	654 error('Non-conforming interfaces not implemented yet.');
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	655 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	656
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	657 % Returns the component number that is the tangential/normal component
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	658 % at the specified boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	659 function comp = getComponent(obj, comp_str, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	660 assertIsMember(comp_str, {'normal', 'tangential'});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	661 assertIsMember(boundary, {'w', 'e', 's', 'n'});
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	662
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	663 switch boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	664 case {'w', 'e'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	665 switch comp_str
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	666 case 'normal'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	667 comp = 1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	668 case 'tangential'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	669 comp = 2;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	670 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	671 case {'s', 'n'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	672 switch comp_str
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	673 case 'normal'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	674 comp = 2;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	675 case 'tangential'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	676 comp = 1;
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	677 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	678 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	679 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	680
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	681 % Returns h11 for the boundary specified by the string boundary.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	682 % op -- string
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	683 function h11 = getBorrowing(obj, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	684 assertIsMember(boundary, {'w', 'e', 's', 'n'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	685
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	686 switch boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	687 case {'w','e'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	688 h11 = obj.h11{1};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	689 case {'s', 'n'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	690 h11 = obj.h11{2};
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	691 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	692 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	693
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	694 % Returns the outward unit normal vector for the boundary specified by the string boundary.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	695 function nu = getNormal(obj, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	696 assertIsMember(boundary, {'w', 'e', 's', 'n'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	697
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	698 switch boundary
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	699 case 'w'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	700 nu = [-1,0];
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	701 case 'e'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	702 nu = [1,0];
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	703 case 's'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	704 nu = [0,-1];
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	705 case 'n'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	706 nu = [0,1];
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	707 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	708 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	709
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	710 % Returns the boundary operator op for the boundary specified by the string boundary.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	711 % op -- string
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	712 function o = getBoundaryOperator(obj, op, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	713 assertIsMember(boundary, {'w', 'e', 's', 'n'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	714 assertIsMember(op, {'e', 'e1', 'e2', 'tau', 'tau1', 'tau2'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	715
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	716 switch op
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	717 case {'e', 'e1', 'e2', 'tau', 'tau1', 'tau2'}
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	718 o = obj.([op, '_', boundary]);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	719 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	720
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	721 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	722
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	723 % Returns the boundary operator op for the boundary specified by the string boundary.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	724 % op -- string
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	725 function o = getBoundaryOperatorForScalarField(obj, op, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	726 assertIsMember(boundary, {'w', 'e', 's', 'n'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	727 assertIsMember(op, {'e'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	728
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	729 switch op
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	730
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	731 case 'e'
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	732 o = obj.(['e_scalar', '_', boundary]);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	733 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	734
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	735 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	736
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	737 % Returns the boundary operator T_ij (cell format) for the boundary specified by the string boundary.
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	738 % Formula: tau_i = T_ij u_j
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	739 % op -- string
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	740 function T = getBoundaryTractionOperator(obj, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	741 assertIsMember(boundary, {'w', 'e', 's', 'n'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	742
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	743 T = obj.(['T', '_', boundary]);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	744 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	745
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	746 % Returns square boundary quadrature matrix, of dimension
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	747 % corresponding to the number of boundary unknowns
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	748 %
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	749 % boundary -- string
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	750 function H = getBoundaryQuadrature(obj, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	751 assertIsMember(boundary, {'w', 'e', 's', 'n'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	752
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	753 H = obj.getBoundaryQuadratureForScalarField(boundary);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	754 I_dim = speye(obj.dim, obj.dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	755 H = kron(H, I_dim);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	756 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	757
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	758 % Returns square boundary quadrature matrix, of dimension
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	759 % corresponding to the number of boundary grid points
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	760 %
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	761 % boundary -- string
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	762 function H_b = getBoundaryQuadratureForScalarField(obj, boundary)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	763 assertIsMember(boundary, {'w', 'e', 's', 'n'})
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	764
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	765 H_b = obj.(['H_', boundary]);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	766 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	767
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	768 function N = size(obj)
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	769 N = obj.dim*prod(obj.m);
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	770 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	771 end
8f4e79aa32ba Add fully compatible D2Variable opSet and first implementation of ElasticAnisotropic Martin Almquist <malmquist@stanford.edu> parents: diff changeset	772 end

Mercurial > repos > public > sbplib

annotate +scheme/Elastic2dVariableAnisotropic.m @ 1335:8d9fc7981796 feature/D2_boundary_opt